Perforation Design Calculator

Shot Density Guidelines

Module 2 — Penetration Depth (API RP 19B Correction)

def penetration_depth_insitu(L_berea_in, UCS_berea_psi=6000,
                              UCS_insitu_psi=8000,
                              overburden_psi=6500, pore_psi=3000,
                              cementation_factor=1.0):
    """
    API RP 19B: in-situ penetration correction.
    Step 1: Rock strength correction
      L_rc = L_berea * (UCS_berea / UCS_insitu)^0.36
    Step 2: Effective stress correction (Berea tested at zero confining pressure)
      sigma_eff = overburden - pore_pressure
      correction = (1 - 0.086 * sqrt(sigma_eff / 1000))
    L_insitu = L_rc * correction * cementation_factor
    All lengths in inches; pressures in psi.
    """
    L_rc = L_berea_in * (UCS_berea_psi / UCS_insitu_psi)**0.36
    sigma_eff = overburden_psi - pore_psi
    stress_corr = 1.0 - 0.086 * (sigma_eff / 1000.0)**0.5
    return L_rc * stress_corr * cementation_factor

Typical Appalachian corrections:

Module 3 — Perforation Skin (Karakas and Tariq, 1991)

Total perforation skin: S_perf = S_H + S_V + S_wb

import math

def horizontal_skin_sh(k_h, k_v, L_perf_in, r_perf_in, h_perf_ft,
                        phasing_deg):
    """
    S_H: horizontal component of perforation skin
    Simplified form (Karakas-Tariq Table 1 constants for phasing):
    S_H = ln(r_w / r'_w)  where r'_w = a1 * exp(a2 * Lp/r_w) * r_w
    Uses phasing-dependent a1, a2 constants from K-T Table 1.
    This is the dominant term for standard completions.
    """
    # Constants from Karakas-Tariq (1991) Table 1
    params = {
        360: (0.250, -2.091, 0.0453),   # 0° phasing
        180: (0.500, -2.025, 0.0943),
        120: (0.648, -2.018, 0.0634),
         90: (0.726, -1.905, 0.1038),
         60: (0.813, -1.898, 0.1023),
    }
    a1, a2, a3 = params.get(phasing_deg, params[90])
    r_w_ft = 0.365   # typical wellbore radius (ft)
    L_perf_ft = L_perf_in / 12.0
    r_perf_ft = r_perf_in / 12.0
    # Effective wellbore radius
    r_w_prime = a1 * r_w_ft * math.exp(a2 * r_perf_ft + a3 * L_perf_ft)
    return math.log(r_w_ft / r_w_prime)

def wellbore_skin_swb(r_perf_in, L_perf_in, r_w_in, spf, phasing_deg):
    """
    S_wb: wellbore skin (near-wellbore damage not cleaned by perfs).
    Typically small for underbalanced perforating; significant for OBP.
    Approximate: S_wb = c1 * exp(c2 * r_w) for phasing-dependent c1, c2.
    """
    c1_c2 = {360: (1.6e-1, 2.675), 180: (2.6e-2, 4.532),
             120: (6.6e-3, 5.320),  90: (1.9e-3, 6.155), 60: (3.0e-4, 7.509)}
    c1, c2 = c1_c2.get(phasing_deg, c1_c2[90])
    r_w_ft = r_w_in / 12.0
    return c1 * math.exp(c2 * r_w_ft)

def total_perforation_skin(S_H, S_V=0.0, S_wb=0.0):
    """S_total = S_H + S_V + S_wb"""
    return S_H + S_V + S_wb

Module 4 — Underbalanced vs. Overbalanced Perforating

Underbalance Pressure Recommendation (King, 1989)

def recommended_underbalance(reservoir_psi, k_md, fluid="gas"):
    """
    Recommended underbalance pressure (psi) to clean perforation tunnels.
    King (1989) empirical:
      Gas wells:  UB = 250 + 5500/k for k < 10 mD
      Oil wells:  UB = 1000 - 200*k for k in [0.01, 5] mD
                  UB = 200 psi minimum
    k_md: formation permeability (mD)
    """
    if fluid.lower() == "gas":
        ub = 250 + 5500.0 / max(k_md, 0.1)
    else:
        ub = max(200.0, 1000.0 - 200.0 * k_md)
    # Don't exceed reservoir pressure
    return min(ub, reservoir_psi * 0.85)

def is_underbalanced(wellbore_psi, reservoir_psi):
    """Simple check: wellbore_psi < reservoir_psi -> underbalanced."""
    return wellbore_psi < reservoir_psi

Selection guidance:

Module 5 — Limited Entry Design (Multi-Cluster Horizontal)

Friction Pressure at Perforation Entry

def perforation_friction_pressure(q_bpm, n_perfs, d_perf_in,
                                   fluid_sg=1.0, Cd=0.9):
    """
    dP_perf = 0.2369 * (rho / Cd^2) * (q / n / d^2)^2
    q_bpm:    total injection rate (bbl/min)
    n_perfs:  total number of perforations in cluster
    d_perf_in: entry hole diameter (inches)
    fluid_sg: fluid specific gravity
    Cd:       discharge coefficient (0.85–0.95 typical)
    Returns: friction pressure (psi) across perforations
    """
    rho_ppg = fluid_sg * 8.34   # lb/gal
    q_per_perf_bpm = q_bpm / n_perfs
    return 0.2369 * (rho_ppg / Cd**2) * (q_per_perf_bpm / d_perf_in**2)**2

Diversion Efficiency (Limited Entry)

def limited_entry_diversion(q_total_bpm, n_clusters, spf_per_cluster,
                              d_perf_in, delta_stress_psi, fluid_sg=1.0,
                              Cd=0.9):
    """
    Equal entry when dP_perf >> delta_stress between clusters.
    Rule of thumb: dP_perf per cluster > 2 × stress contrast to ensure
    >80% of clusters accept fluid.
    Returns: dP_perf for a single cluster and diversion ratio estimate.
    """
    n_perfs_cluster = spf_per_cluster
    q_per_cluster_bpm = q_total_bpm / n_clusters
    dp = perforation_friction_pressure(q_per_cluster_bpm,
                                        n_perfs_cluster, d_perf_in,
                                        fluid_sg, Cd)
    ratio = dp / delta_stress_psi if delta_stress_psi > 0 else float("inf")
    efficiency = min(1.0, 0.5 + 0.5 * min(ratio / 2.0, 1.0))
    return {"dP_perf_psi": dp, "diversion_ratio": ratio,
            "estimated_cluster_efficiency": efficiency}

Appalachian limited entry parameters:

• Typical stress contrast between clusters: 200–800 psi
• Target dP_perf: 500–1,500 psi for adequate diversion
• Entry hole diameter: 0.38"–0.50" for most perforating charges at 2–4 SPF

Output Format

## Perforation Design — [Well / Zone]
**Formation:** [Name] | **Depth:** X,XXX–X,XXX ft | **k:** X.X mD

### Gun/Charge Selection
| Parameter | Value |
|-----------|-------|
| Charge type | [API RP 19B class] |
| Berea penetration (in) | |
| In-situ penetration (in) | [corrected] |
| Entry hole diameter (in) | |
| Shot density (SPF) | |
| Phasing | |

### Perforation Skin Summary
| Component | Value |
|-----------|-------|
| S_H (horizontal) | |
| S_V (vertical) | |
| S_wb (wellbore) | |
| S_perf (total) | |

### Underbalance Assessment
| Recommended UB (psi) | Achievable UB (psi) | Method |
|---------------------|--------------------|----|
| | | UBP / OBP + acid |

### Limited Entry (Horizontal)
| Cluster spacing (ft) | SPF/cluster | dP_perf (psi) | Stress contrast (psi) | Efficiency |
|---------------------|------------|--------------|----------------------|------------|
| | | | | |

Error Handling

Caveats

• Karakas-Tariq skin equations are analytical and assume uniform perforation tunnel penetration. In reality, tunnels vary due to rock heterogeneity and gun eccentricity.
• API RP 19B Berea strength correction is an empirical approximation. Lab testing of actual formation core is more accurate for penetration prediction.
• Limited entry diversion efficiency assumes uniform stress contrast across clusters. Natural fractures and local heterogeneity can override designed diversion.
• Perforation friction pressure equations assume Newtonian fluid. For viscoelastic frac fluids, apparent viscosity at perforation velocity is typically much higher — dP_perf will be larger (better diversion).
• Near-wellbore tortuosity (not captured here) can dominate treating pressure in tight formations; evaluate with step-down test after perforating.